Question

If x = 3 + 2 √2 , then find the value of x + 1 / x .

Answer 1

Answer:

8 x

Step-by-step explanation:

I hope it is correct answer

Answer 2

If x = 3 + 2√2 ; we need to x + 1/x .

As learnt in rationalising the denominator ; we can consider consider:

$\small{\longrightarrow{\sf{\dfrac{1}{x} = \dfrac{1}{3 + 2 \sqrt{2} }}}}$ .

Now we need to rationalize the denominator using the following steps :

1. Take the opposite sign of the denominator and multiply it with both the numerator as well as the denominator.
2. This create an identity of (a+b)(a-b) in the denominator.
3. Then expand into a² - b² and simplify .

Rationalising the denominator :

$\small{\longrightarrow{\sf{\dfrac{1}{3 + \sqrt{2}} \times \dfrac{3 - 2 \sqrt{2}}{3 - 2 \sqrt{2}}}}}$

a = 3

b = 2√2

$\small{\longrightarrow{\sf{\dfrac{3 - 2 \sqrt{2}}{{(3)}^{2} - {(2 \sqrt{2})}^{2}}}}}$

The root symbol and power of 2 cut either.

$\small{\longrightarrow{\sf{\dfrac{3 - 2 \sqrt{2}}{9 - (2 \times 2 \times 2}}}}$

$\small{\longrightarrow{\sf{\dfrac{3 - 2 \sqrt{2}}{9 - 8}}}}$

$\small{\longrightarrow{\sf{\dfrac{3 - 2 \sqrt{2}}{1}}}}$

The obtained number can also be written as :

3 - 2√2 that is without the denominator 1 .

Now according to the question ; we need to do :

$\small{\sf{x + 1/x}}$

x is already given and we have found 1/x .

So :

$\small{\longrightarrow{\sf{3 + \cancel{2 \sqrt{2}} (+) 3 - \cancel{2 \sqrt{2}}}}}$

Both the 2√2 and -2√2 get cancelled due to their opposite signs.

$\small{\longrightarrow{\sf{3 + 3}}}$

$\implies{\large{\boxed{\sf{6}}}}$